Hard rock mining company is interested in coming up with formulas that will be used to base management planning and decision making. The purpose of this paper is to determine the factors that affect the utility costs and we will be using regression analysis to determine the strength of the relationship between the utility cost which is the outcome variable and the predictor variables direct labor hours and tons mined. The objective of this analysis is to consider the independent variable that is statistically significant in the prediction of the dependent variable. The summary statistics of the variables and the formulas for computing them is detailed below.
The hypothesis being tested is;
H0 – There is no relationship between the dependent variable and the predictor variables.
Ha – There is a relationship between the dependent variable and the predictor variable.
The hypothesis being tested is
H0 – The coefficients of the predictor variable are all equal to zero β1 = β2 = 0
Ha – The coefficients of the predictor variables are not all equal to zero β ≠ 0
Interpretation
The hypothesis being tested is to determine if the predictor variables can be used to predict the outcome variable. The test statistic is the F-statistic whose p-value is 0.001. The test is significant given that the p-value is less than the significance level as such we reject the null hypothesis that there is no relationship between the independent variables and the dependent variable. The alternative hypothesis is accepted and it is concluded that there is a relationship between the dependent variable and the predictor variables. The relationship is used to develop a standardized regression equation that will be used to compute utility cost when the other variables are known.
The null hypothesis in the test to determine the coefficients of the predictor variables is rejected at α = 0.05. The test for the Tons mined is insignificant because the p-value = 0.585 > 0.05. We therefore fail to reject the hypothesis that the coefficient of Tons mined is significantly equal to zero. As a consequence, the variable Tons mined will not be used in the prediction of the variable utilities cost. The test for the variable Direct labor hours is significant p-value = 0.002 < 0.05. Therefore, we reject the null hypothesis that the coefficient of the variable direct labor hours is significantly equal to zero. The variable direct labor will be used in the prediction of the variable utility cost. The constant is also insignificant and as such it will not be used in the standardized regression equation.
The regression equation is Utility cost = 8.477 (Direct Labor-Hours)
The correlation coefficient is 0.969 which indicates a strong linear relationship between utility cost and direct labor-hours. The coefficient of determination R2 = 0.939 which shows that 93.9% of the variance of utility cost can be explained by the variance of the direct labor-hours.
Conclusion.
The production superintendent was corrected in estimating that that direct labor hours is a better base in the formulation of a formula used to predict utility costs. The strong positive correlation between the utility cost and the direct labor hours and the statistical significance improves the reliability of the estimate made using the standardized regression equation.
